Self isothermal growth

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

Figure 24. Streamlines and isotherms for the growth of silicon in a prototype Czochralski system with self-consistent calculation of interface and crystal shapes by using the quasi steady-state thermal-capillary model and the condition that the crystal radius remains constant. Calculations are for decreasing melt volume. The Grashof number (scaled with the maximum temperature difference in the melt) varies between 1.0 X 107 and 2.0 X 107 with decreasing...

Polymer crystallization is a typical first-order phase transition, following the nucleation and growth mechanism. Therefore, when isothermal crystallization happens slowly at high temperatures, one can observe a significantly long incubation period for crystal nucleation, followed by a self-acceleration process for crystal growth. This process is illustrated by the time-evolution curve of volume crystallinity in Pig. 10.21. 

The ideal self-nucleation temperature is probably the best possible choice, because the use of the ideal self-nucleation temperature will provide the polymer with an extremely high nucleation density (typically on the order of 10 nuclei/cm ), which can produce a full completion of the nucleation step before any isothermal crystallization is performed. This novel treatment could be used to study the relative contributions of nucleation and growth in semicrystalline homopolymers and semicrystalline components within diblock copolymers or polyblends. 

Figure 11.8a shows the overall crystallization kinetics of PPDX obtained by DSC for neat and self-nucleated samples. When the sample is self-nucleated, the isothermal DSC data contain information of crystal growth only (assuming the self-nucleation process applied was 100% efficient in creating all necessary nuclei previously). In fact, the acceleration of the overall crystallization kinetics caused by the self-nucleation treatment is evident in Figure 11.8a, because the rates are higher for the self-nucleated sample as compared to neat PPDX at identical crystallization temperatures and also crystallization at lower supercoolings can be achieved in the self-nucleated samples. 

The results presented in Table 11.4 are fully consistent with our hypothesis of possible separation of primary nucleation and growth contributions, as schematically represented in Figure 11.10. The Kg value obtained by the LH model for PPDX is reduced from 31.0 to 17.0 (xl0 K ) once the self-nucleation step is performed before the isothermal crystallization (see Table 11.4). This indicates that the energy barrier for primary nucleation is about 14.0 X 10" K in other words, the energy barrier for nucleation of the PPDX is about 45% of the total energy barrier for the overall crystallization process. 

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